Question 112
Let $\left(a_{n}\right)_{n \geqslant 1}$ be a sequence of positive integers such that $a_{1}$ and $a_{2}$ are coprime and, for every $n \geqslant 1$, $a_{n+2}=a_{n} a_{n+1}+1$. Show that for every integer $m\gt 1$, there exists $n\gt m$ such that $a_{m}^{m} \mid a_{n}^{n}$. Is the result still true when $m=1$?